Abstract and Applied Analysis
Volume 2008 (2008), Article ID 628178, 8 pages
On the Stability of Quadratic Functional Equations
1Department of Mathematics, Daejin University, Kyeonggi 487-711, South Korea
2Department of Mathematics Education, Pusan National University, Pusan 609-735, South Korea
3Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
Received 5 October 2007; Revised 27 November 2007; Accepted 4 January 2008
Academic Editor: Paul Eloe
Copyright © 2008 Jung Rye Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be vector spaces and a fixed positive integer. It is shown that a mapping for all if and only if the mapping satisfies for all
. Furthermore, the Hyers-Ulam-Rassias stability of the above functional
equation in Banach spaces is proven.